Three-dimensional Spatial Interpolation Method for Site Soil Pollutant Concentrations Integrating Multi-source Collaborative Variables

Abstract

The present invention relates to a three-dimensional spatial interpolation method for site soil pollutant concentrations that integrates multi-source collaborative variables, including: 1. Collection of borehole soil pollutant concentration data and multi-source collaborative variable data; 2. Extraction of principal components of collaborative variables; 3. Screening of principal components of collaborative variables; 4. Calculation of the Mahalanobis distance between the three-dimensional grid to be interpolated and the collaborative variables at the soil sampling points, as well as the Euclidean distance between their three-dimensional coordinate positions; 5. Summing the p-th power of the Mahalanobis distance between collaborative variables and the p-th power of the Euclidean distance between three-dimensional coordinate positions according to a certain weight ratio α, and then taking the reciprocal as the interpolation weight to construct a three-dimensional interpolation model that integrates multi-source collaborative variables; 6. Using simulated annealing to optimize the parameters α and p, and performing three-dimensional interpolation using the interpolation model with optimized parameters; the entire design scheme can significantly improve the three-dimensional interpolation accuracy of sparse borehole soil pollution data and the details of spatial distribution characterization, and has broad application prospects.

Description

Technical Field

[0001] The present invention relates to a three-dimensional spatial interpolation method for site soil pollutant concentrations integrating multi-source collaborative variables, and belongs to the technical field of soil pollution prediction. Background Art

[0002] Accurately depicting the three-dimensional spatial distribution of site soil pollutant concentrations is an urgent need for site pollution risk assessment and pollution remediation. In current site investigation and pollution risk mapping practice, spatial interpolation methods based on the principle of "the closer the distance, the more similar" are mainly used to interpolate and predict the three-dimensional spatial distribution of soil pollutant concentrations. Among them, the most widely used three-dimensional spatial interpolation methods mainly include the three-dimensional inverse distance weighting interpolation method (Inverse Distance Weighting, IDW) and the three-dimensional ordinary kriging interpolation method (Ordinary Kriging, OK), etc. However, the current spatial interpolation methods still have the following deficiencies in the spatial prediction of site soil pollutant concentrations:

[0003] (1) The spatial distribution pattern of site soil pollutants is extremely complex, and the situation of "the two points are very close, but the difference in their pollutant concentrations is extremely significant" is common, making it difficult to fully meet the principle of "the closer the distance, the more similar" of the IDW and OK interpolation methods, resulting in a large error in the interpolation results of soil pollutant concentrations.

[0004] (2) Due to the economic and time cost constraints of borehole sampling and sample laboratory analysis, the number of boreholes in pollution site investigation may be relatively sparse. The IDW interpolation method only considers the influence of the Euclidean distance of sample points in the geographical space on the spatial interpolation weight, resulting in a strong smoothing effect on its interpolation results and being difficult to reflect the detailed characteristics of local spatial variation of pollutant concentrations. At the same time, under the condition of sparse boreholes, due to the small number of pairs of soil sample points with different spacings, there is great uncertainty in the inference of the semi-variogram function of soil pollutant concentrations, resulting in poor reliability of the interpolation results of the OK interpolation method and being difficult to apply.

[0005] (3) In site investigation, although the number of boreholes may be relatively sparse, a lot of collaborative variable data related to pollutant concentrations can still be obtained, such as site functional area layout maps, stratigraphic structures, conductivity and resistivity distribution maps of geophysical exploration, etc. However, under the condition of sparse boreholes, the existing spatial interpolation methods are still difficult to integrate these multi-source collaborative variable data, thus restricting the improvement of spatial interpolation accuracy. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a three-dimensional spatial interpolation method for site soil pollutant concentrations integrating multi-source collaborative variables, adopting a new design strategy, which can effectively improve the efficiency of spatial prediction of soil pollutant concentrations.

[0007] The present invention adopts the following technical solutions to solve the above technical problems: The present invention designs a three-dimensional spatial interpolation method for the concentration of soil pollutants in a site by integrating multi-source collaborative variables. Through steps A to G, a three-dimensional interpolation model for the concentration of soil pollutants in the target area is obtained. Through step i, the three-dimensional interpolation model for the concentration of soil pollutants is applied to predict the three-dimensional distribution of the concentration of soil pollutants in the underground space of the target area;

[0008] Step A. Obtain the measured values of the concentrations of soil pollutants at soil sample points at each preset depth under each preset drilling position in the target area, and a multi-source collaborative variable data set corresponding to the target area that includes each preset data type, and then proceed to step B;

[0009] Step B. Based on the three-dimensional rasterized underground space preset in the target area, obtain the multi-source collaborative variable data sets corresponding to each grid in the underground space of the target area, and use the principal component analysis method to obtain the scores of the principal components of each collaborative variable in the multi-source collaborative variable data set. Then, according to the positions of the soil sample points, obtain the scores of the principal components of each collaborative variable corresponding to each soil sample point, and then proceed to step C;

[0010] Step C. Based on each soil sample point, perform stepwise regression analysis with the scores of the principal components of each collaborative variable corresponding to the soil sample point as independent variables and the measured values of the soil pollutant concentration as the dependent variable, screen the principal component data of each collaborative variable, and obtain each principal component that is significantly correlated with the soil pollutant concentration, forming each collaborative variable, and then proceed to step D;

[0011] Step D. Based on each collaborative variable, obtain the collaborative variable vectors composed of the data of each collaborative variable corresponding to each grid, and obtain the collaborative variable vectors composed of the data of each collaborative variable corresponding to each soil sample point, and then proceed to step E;

[0012] Step E. Obtain the Mahalanobis distances between the collaborative variable vectors corresponding to each grid and the collaborative variable vectors corresponding to each soil sample point, and obtain the three-dimensional Euclidean distances between each grid and each soil sample point, and then proceed to step F;

[0013] Step F. According to each Mahalanobis distance, each three-dimensional Euclidean distance, and the weight ratio parameter α and the distance power parameter p, construct a three-dimensional interpolation model for the soil pollutant concentration, and then proceed to step G;

[0014] Step G. Use the simulated annealing algorithm to optimize and obtain the value of the weight ratio parameter α and the value of the distance power parameter p in the three-dimensional interpolation model for the soil pollutant concentration, that is, obtain the three-dimensional interpolation model for the soil pollutant concentration corresponding to the target area;

[0015] Step i: For each grid in the underground space of the target area, apply the three-dimensional interpolation model of soil pollutant concentration to obtain the predicted value of soil pollutant concentration for the grid, that is, realize the three-dimensional prediction of soil pollutant concentration in the underground space of the target area.

[0016] As a preferred technical solution of the present invention: It further includes the following Step H. After Step G is executed, enter Step H;

[0017] Step H: Apply the cross-validation method to calculate the root mean square error between the predicted value of soil pollutant concentration of the soil sample points obtained based on the three-dimensional interpolation model of soil pollutant concentration and the measured value of the corresponding soil pollutant concentration, that is, obtain the interpolation accuracy of the three-dimensional interpolation model of soil pollutant concentration.

[0018] As a preferred technical solution of the present invention: The preset data types included in the multi-source collaborative variable data set are the distribution of site functional area types, the distribution of soil resistivity inversed by geophysical exploration, and the distribution of soil conductivity inversed by geophysical exploration.

[0019] As a preferred technical solution of the present invention: Step E includes the following Steps E1 to E2:

[0020] Step E1: First, for each grid in the underground space of the target area, according to the following formula:

[0021]

[0022] Obtain the Mahalanobis distance (MD ij ) I×J between the collaborative variable vectors corresponding to each grid and the collaborative variable vectors corresponding to each soil sample point, where i = 1, 2,..., I, I represents the number of grids in the underground space of the target area, j = 1, 2,..., J, J represents the number of soil sample points in the target area, cov i represents the collaborative variable vector corresponding to the i-th grid in the underground space of the target area, cov j represents the collaborative variable vector corresponding to the j-th soil sample point in the target area, ∑ represents the covariance matrix, (·) T represents the transpose, and MD ij represents the Mahalanobis distance between the collaborative variable vector corresponding to the i-th grid in the underground space of the target area and the collaborative variable vector corresponding to the j-th soil sample point in the target area;

[0023] At the same time, for each grid in the underground space of the target area, according to the following formula:

[0024]

[0025] Obtain the three-dimensional Euclidean distance (ED ij ) I×J between each grid and each soil sampling point, where (x 1，i , x 2，i , x 3，i ) represents the three-dimensional coordinates of the i-th grid in the underground space of the target area, and (y 1，j , y 2，j , y 3，j ) represents the three-dimensional coordinates of the j-th soil sampling point in the target area; then proceed to step E2;

[0026] Step E2. Normalize each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J to the same scale, and update each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J , then proceed to step F.

[0027] As a preferred technical solution of the present invention: in the said step F, according to each Mahalanobis distance (MD ij ) I×J , each Euclidean distance (ED ij ) I×J , as well as the weight ratio parameter α and the distance power parameter p, construct the three-dimensional interpolation model of soil pollutant concentration as follows:

[0028]

[0029] Then proceed to step G, where P i represents the predicted value of the soil pollutant concentration of the i-th grid in the underground space of the target area, and V j represents the measured value of the soil pollutant concentration of the j-th soil sampling point in the target area.

[0030] As a preferred technical solution of the present invention: in the said step G, based on the prior value range [1, 3] of the distance power parameter p and the prior value range [0, 1] of the weight ratio parameter α, use the simulated annealing algorithm to optimize and obtain the values of the weight ratio parameter α and the distance power parameter p in the three-dimensional interpolation model of soil pollutant concentration.

[0031] As a preferred technical solution of the present invention: in the step i, when applying the three-dimensional interpolation model of soil pollutant concentration to realize the prediction of soil pollutant concentration in the underground space of the target area, if both the Euclidean distance between the grid and the nearest soil sample point and the Mahalanobis distance between the co-variables are less than or respectively equal to the preset corresponding thresholds, then the measured value of the soil pollutant concentration of this soil sample point is defined as the predicted value of the soil pollutant concentration of this grid.

[0032] Compared with the prior art, the three-dimensional spatial interpolation method for site soil pollutant concentration integrating multi-source co-variables of the present invention has the following technical effects by adopting the above technical solution:

[0033] The three-dimensional spatial interpolation method for site soil pollutant concentration integrating multi-source co-variables designed by the present invention adopts a brand-new design strategy. By the Mahalanobis distance of multi-source co-variables in the attribute space, the interpolation weight ratio at the position of the three-dimensional grid to be interpolated by the three-dimensional inverse distance weighted interpolation method is corrected, so as to realize the integration of multi-source co-variable data in the spatial interpolation method. Under the condition of sparse boreholes on the site, a three-dimensional spatial distribution interpolation result of soil pollutant concentration with higher precision can be obtained, which helps to reduce the mapping cost of site pollution risk; and for the parameters of the designed spatial interpolation method, the simulated annealing algorithm is used for optimization, which can effectively reduce the influence of the artificial setting of interpolation parameters on the interpolation accuracy. Description of the Drawings

[0034] Figure 1 is a flowchart of the specific implementation process of the three-dimensional interpolation method of the present invention

[0035] Figure 2 is a flowchart of optimizing the parameters α and p of the three-dimensional interpolation model by the simulated annealing algorithm;

[0036] Figure 3 is a spatial distribution map of soil boreholes in a polluted site of a certain site;

[0037] Figure 4 is a spatial distribution map of the conductivity of a polluted site of a certain site;

[0038] Figure 5 is a spatial distribution map of the resistivity of a polluted site of a certain site;

[0039] Figure 6 is a curve of the root mean square error of the interpolation model corresponding to the accepted parameter values changing with the number of iterations of the simulated annealing;

[0040] Figure 7a is the three-dimensional spatial distribution map of the soil Cr 6+ concentration predicted by the three-dimensional interpolation method of the present invention;

[0041] Figure 7bIt is the three-dimensional spatial distribution map of the soil Cr concentration in a contaminated plot predicted by the traditional IDW interpolation method. 6+ Concentration Specific implementation manners

[0042] The following further details the specific implementation manners of the present invention in conjunction with the accompanying drawings of the specification.

[0043] The present invention designs a three-dimensional spatial interpolation method for the soil pollutant concentration in a site by integrating multi-source collaborative variables. In practical applications, as Figure 1 shown, through the following steps A to G, a three-dimensional interpolation model of the soil pollutant concentration in the target area is obtained.

[0044] Step A. Obtain the measured values of the soil pollutant concentrations of the soil sample points at each preset depth under each preset borehole position in the target area, and the multi-source collaborative variable dataset corresponding to the target area including each preset data type, and then proceed to step B.

[0045] In applications, regarding each preset data type included in the multi-source collaborative variable dataset, it is designed to include the distribution of the site functional area type, the soil resistivity distribution inversed by geophysical exploration, and the soil conductivity distribution inversed by geophysical exploration. The collaborative variable data from multiple sources helps to reflect the spatial variation characteristic information of the soil pollutant concentration from different perspectives.

[0046] Step B. Based on the preset three-dimensional rasterized underground space in the target area, obtain the multi-source collaborative variable datasets corresponding to each grid in the underground space of the target area, and use the principal component analysis method to obtain the scores of the principal components of each collaborative variable in the multi-source collaborative variable dataset. Then, according to the positions of the soil sample points, obtain the scores of the principal components of each collaborative variable corresponding to each soil sample point, and then proceed to step C.

[0047] Since there may be correlations between the original data of each collaborative variable (i.e., there may be a situation of information redundancy), among the principal components of the collaborative variables extracted by the principal component analysis method, it can be ensured that they are mutually independent, thereby reducing information redundancy.

[0048] Step C. Based on each soil sample point, perform stepwise regression analysis with the scores of the principal components of each collaborative variable corresponding to the soil sample point as independent variables and the measured values of the soil pollutant concentration as the dependent variable, screen the principal component data of each collaborative variable, obtain the principal components that are significantly correlated with the soil pollutant concentration, and form each collaborative variable, and then proceed to step D.

[0049] Step D. Based on each collaborative variable, obtain the collaborative variable vectors composed of the collaborative variable data corresponding to each grid and the collaborative variable vectors composed of the collaborative variable data corresponding to each soil sample point, and then proceed to step E.

[0050] Step E. Obtain the Mahalanobis distance between the co-variable vectors corresponding to each grid and the co-variable vectors corresponding to each soil sample point, and obtain the three-dimensional Euclidean distance between each grid and each soil sample point, and then proceed to Step F.

[0051] In practical applications, the above Step E includes the following Steps E1 to E2.

[0052] Step E1. First, for each grid in the underground space of the target area respectively, according to the following formula:

[0053]

[0054] Obtain the Mahalanobis distance (MD ij ) I×J between the co-variable vectors corresponding to each grid and the co-variable vectors corresponding to each soil sample point, where i = 1, 2,..., I, I represents the number of grids in the underground space of the target area, j = 1, 2,..., J, J represents the number of soil sample points in the target area, cov i represents the co-variable vector corresponding to the i-th grid in the underground space of the target area, cov j represents the co-variable vector corresponding to the j-th soil sample point in the target area, ∑ represents the covariance matrix, (·) T represents the transpose, and MD ij represents the Mahalanobis distance between the co-variable vector corresponding to the i-th grid in the underground space of the target area and the co-variable vector corresponding to the j-th soil sample point in the target area.

[0055] The Mahalanobis distance reflects the similarity degree between the co-variable vectors of the three-dimensional grid to be interpolated and the soil sample points. That is, the smaller the Mahalanobis distance between the co-variable vectors of two points, the more similar their co-variable vectors are. Since there is a certain correlation between the selected co-variables and the soil pollutant concentration, therefore, the more similar the co-variable vectors of two points are, the closer their soil pollutant concentrations are, thus reflecting the prior information of the spatial distribution difference of soil pollutant concentrations contained in the co-variable vectors.

[0056] At the same time, for each grid in the underground space of the target area respectively, according to the following formula:

[0057]

[0058] Obtain the three-dimensional Euclidean distance (ED ij ) I×J between each grid and each soil sample point, where (x 1，i , x 2，i , x 3，i ) represents the three-dimensional coordinates of the i-th grid in the underground space of the target area, (y1，j , y 2，j , y 3，j ) represents the three-dimensional coordinates of the j-th soil sample point in the target area; then proceed to step E2.

[0059] Step E2. Normalize each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J to the same scale, and update each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J , and then proceed to step F, and apply medium design to normalize to between [0, 1] to ensure that the Mahalanobis distance and the Euclidean distance are on the same scale.

[0060] The core idea of constructing a three-dimensional interpolation model integrating multi-source collaborative variables in the present invention is to correct the interpolation weight ratio of IDW interpolation at the position of the three-dimensional grid to be interpolated through the Mahalanobis distance of multi-source collaborative variables in the attribute space, so as to realize the integration of multi-source collaborative variable data in the spatial interpolation method.

[0061] Step F. According to each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J , as well as the weight ratio parameter α and the distance power parameter p, construct the three-dimensional interpolation model of soil pollutant concentration as follows:

[0062]

[0063] Then proceed to step G, where P i represents the predicted value of the soil pollutant concentration of the i-th grid in the underground space of the target area, and V j represents the measured value of the soil pollutant concentration of the j-th soil sample point in the target area.

[0064] It can be seen from the three-dimensional interpolation model of soil pollutant concentration integrating multi-source collaborative variables in the present invention that the advantage of the present invention is that it can adjust the influence degree of its spatial interpolation weight by controlling the ratio of the Mahalanobis distance of collaborative variables to the three-dimensional Euclidean distance, so as to make full use of the multi-source collaborative variable information of site pollution and improve the spatial interpolation accuracy of pollutant concentration data of sparse boreholes.

[0065] Step G. As Figure 2As shown, based on the prior value range [1, 3] of the distance power parameter p and the prior value range [0, 1] of the weight ratio parameter α, the simulated annealing algorithm is used to optimize and obtain the value of the weight ratio parameter α and the value of the distance power parameter p in the three-dimensional interpolation model of soil pollutant concentration, that is, to obtain the three-dimensional interpolation model of soil pollutant concentration corresponding to the target area, and then step H is entered.

[0066] Step H. Apply a cross-validation method such as ten-fold cross-validation or leave-one-out cross-validation to calculate the root mean square error between the predicted value of soil pollutant concentration of the soil sample points obtained based on the three-dimensional interpolation model of soil pollutant concentration and the measured value of the corresponding soil pollutant concentration, that is, to obtain the interpolation accuracy of the three-dimensional interpolation model of soil pollutant concentration.

[0067] Based on the three-dimensional interpolation model of soil pollutant concentration obtained above, through step i, the three-dimensional distribution prediction of soil pollutant concentration in the underground space of the target area is realized.

[0068] Step i. For each grid in the underground space of the target area, apply the three-dimensional interpolation model of soil pollutant concentration to obtain the predicted value of soil pollutant concentration of the grid, that is, to realize the three-dimensional prediction of soil pollutant concentration in the underground space of the target area.

[0069] Among them, in the process of applying the three-dimensional interpolation model of soil pollutant concentration to realize the prediction of soil pollutant concentration in the underground space of the target area, if the Euclidean distance between the grid and the nearest soil sample point and the Mahalanobis distance between the co-variables are both less than or respectively equal to the preset corresponding thresholds, then the measured value of soil pollutant concentration of this soil sample point is defined as the predicted value of soil pollutant concentration of this grid.

[0070] In practical applications, taking the three-dimensional spatial interpolation of soil Cr 6+ concentration in a chromium-polluted plot of a chemical plant as an example for illustration, it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0071] The embodiment is a chromium-polluted plot of a chemical plant, and the characteristic pollutant is Cr 6+ , and the three-dimensional interpolation method of the present invention is used to perform three-dimensional spatial interpolation on soil Cr 6+ concentration. The specific process is as follows:

[0072] Step A. Obtain the measured values of soil pollutant concentration of soil sample points at each preset depth under each preset drilling position in the target area, and a multi-source co-variable data set corresponding to the target area including each preset data type, and then enter step B.

[0073] (1) Collection of measured values of soil pollutant concentration: In this example, a total of 34 soil sample points of Cr at each preset depth under 10 drilling positions are collected.6+ Measured concentration data. The maximum sampling depth under the drilling positions is 19.5 m, and the number of drill holes is relatively sparse. Among them, the distribution of soil sample points at each preset depth under each drilling position is as Figure 3 shown;

[0074] (2) Collection of multi-source collaborative variable datasets: The collected collaborative variable data includes the distance from the underground three-dimensional grid to the chromate production workshop, 5 underground conductivity distribution maps obtained at different detection frequencies by induction electromagnetic method (EM), as Figure 4 shown, and the underground resistivity distribution map obtained by detecting and inverting the high-density resistivity method (ERT) as Figure 5 shown, with a total of 7 collaborative variables.

[0075] Step B. Based on the preset three-dimensional rasterized underground space of the target area, obtain the multi-source collaborative variable datasets corresponding to each grid in the underground space of the target area, and use the principal component analysis method to obtain the scores of the principal components of each collaborative variable in the multi-source collaborative variable dataset. Then, according to the positions of the soil sample points, obtain the scores of the principal components of each collaborative variable corresponding to each soil sample point, and then enter Step C.

[0076] (1) According to the boundary range and size of the polluted plot, divide the underground space of the plot into a three-dimensional grid with a grid size of 1 m × 1 m × 1 m (length, width, depth), and a total of 720,500 three-dimensional grids are planned to be divided for subsequent data processing, analysis, and spatial interpolation.

[0077] (2) Use spatial extraction analysis to obtain the collaborative variable values corresponding to each three-dimensional grid, and form a multi-source collaborative variable dataset at the grid to be interpolated. Among them, there are a total of 720,500 three-dimensional grids, and each grid corresponds to 7 collaborative variable values.

[0078] (3) Use the principal component analysis method to perform principal component analysis on the 7 collaborative variable data of 720,500 grids, and a total of 5 principal components of collaborative variables with eigenvalues ≥ 1 are extracted.

[0079] Step C. Based on each soil sample point, perform stepwise regression analysis with the scores of the principal components of each collaborative variable corresponding to the soil sample point as the independent variable and the measured value of the soil pollutant concentration as the dependent variable, screen the principal component data of each collaborative variable, obtain each principal component that is significantly correlated with the soil pollutant concentration, and form each collaborative variable, and then enter Step D.

[0080] (1) Use spatial extraction analysis to obtain the scores of the 5 principal components of collaborative variables corresponding to 34 soil sample points;

[0081] (2) For the 34 soil sampling points of Cr 6+The concentration was used as the dependent variable, and the scores of the 5 co-variable principal components were used as the independent variables for stepwise regression analysis. Under the condition that the significance p-value was 0.05, a total of 2 principal components significantly correlated with the Cr 6+ concentration were selected, and these 2 principal components would be used as co-variables for constructing the subsequent three-dimensional spatial interpolation model.

[0082] Step D. Based on each co-variable, obtain the co-variable vectors composed of the co-variable data corresponding to each grid, and obtain the co-variable vectors composed of the co-variable data corresponding to each soil sampling point, and then proceed to Step E.

[0083] Step E. Obtain the Mahalanobis distances between the co-variable vectors corresponding to each grid and the co-variable vectors corresponding to each soil sampling point, and obtain the three-dimensional Euclidean distances between each grid and each soil sampling point, and then proceed to Step F.

[0084] (1) For the three-dimensional grid of the underground space of the 1m×1m×1m polluted plot, construct co-variable vectors with the co-variables of the 2 selected principal components, and calculate the Mahalanobis distance matrix (MD ij ) 720500×34 between the co-variables of the 720,500 three-dimensional grid positions to be interpolated and the co-variables of the 34 soil sampling point positions (i = 1, 2, 3,..., 720500; j = 1, 2, 3,..., 34)

[0085] (2) For the three-dimensional grid of the underground space of the 1m×1m×1m polluted plot, calculate the Euclidean distance matrix (ED ij ) 720500×34 between the three-dimensional coordinates of the 720,500 three-dimensional grid positions to be interpolated and the 34 soil sampling points (i = 1, 2, 3,..., 720500; j = 1, 2, 3,..., 34).

[0086] (3) Consider the elements in the Mahalanobis distance matrix between co-variables and the Euclidean distance matrix between three-dimensional coordinate positions as a whole respectively, and normalize them to between [0, 1] respectively to ensure that the Mahalanobis distance and the Euclidean distance are on the same scale.

[0087] Step F. According to each Mahalanobis distance (MD ij ) I×J , each Euclidean distance (ED ij ) I×J , as well as the weight ratio parameter α and the distance power parameter p, construct a three-dimensional interpolation model for soil pollutant concentration, and then proceed to Step G.

[0088] Step G. Using the simulated annealing algorithm, optimize to obtain the values of the weight ratio parameter α and the distance power parameter p in the three-dimensional interpolation model of soil pollutant concentration, that is, obtain the three-dimensional interpolation model of soil pollutant concentration corresponding to the target area.

[0089] Step H. Apply the cross-validation method to calculate the root mean square error between the predicted values of soil pollutant concentration at soil sampling points obtained based on the three-dimensional interpolation model of soil pollutant concentration and their corresponding measured values of soil pollutant concentration, that is, obtain the interpolation accuracy of the three-dimensional interpolation model of soil pollutant concentration.

[0090] (1) With [1, 3] as the prior range of the distance power parameter p and [0, 1] as the prior range of the weight ratio parameter α, based on 10-fold cross-validation, use the simulated annealing algorithm to optimize the parameters α and p in the three-dimensional interpolation model.

[0091] In this example, the initial temperature of simulated annealing is set to 10 °C and the number of iterations is set to 2000 times. During the simulated annealing iteration process, for the accepted model parameter values, integrate the Cr 6+ concentration 10-fold cross-validation root mean square error (RMSE) change process as Figure 6 shown. The optimal value of the weight ratio parameter α determined by simulated annealing is 0.928, and the optimal value of the distance power p is 1.91. Based on the optimized parameter values, the three-dimensional distribution of the Cr 6+ concentration predicted by the integrated multi-source collaborative variable three-dimensional space interpolation method is as Figure 7a shown. For comparison, in this example, the traditional three-dimensional IDW interpolation is also used to predict the three-dimensional space distribution of soil Cr 6+ in this polluted plot (where the optimal value of the IDW interpolation inverse distance power determined based on the same cross-validation data is 1.4), and the result is as Figure 7b shown.

[0092] From Figure 7a and Figure 7b it can be seen that although the overall distribution patterns of the Cr 6+ concentration spatial distributions predicted by the two three-dimensional interpolation methods are similar, compared with the smooth interpolation results of the traditional IDW interpolation method, the integrated multi-source collaborative variable three-dimensional interpolation method provided by the present invention can reflect more local spatial variation detail characteristics of the Cr 6+ concentration.

[0093] (2) Use the RMSE calculated by 10-fold cross-validation to evaluate the three-dimensional interpolation accuracy. In this example, the Cr 6+The RMSE of 10-fold cross-validation for concentration is 815.9 mg / kg. Based on the same cross-validation data, the RMSE predicted by the traditional IDW interpolation model is 911.5 mg / kg. Compared with the traditional IDW interpolation method, the prediction error of the integrated multi-source collaborative variable three-dimensional interpolation method proposed by the present invention is reduced by 10.5%. Therefore, it has higher spatial interpolation accuracy.

[0094] The integrated multi-source collaborative variable three-dimensional spatial interpolation method provided by the present invention effectively overcomes the technical bottleneck problems such as the low accuracy of the traditional IDW three-dimensional interpolation method and the insufficient description of the local spatial variation details of pollutant concentration under the condition of sparse borehole data. The integrated multi-source collaborative variable three-dimensional interpolation method provided by the present invention makes full use of the prior information of the spatial distribution of pollutants contained in the easily accessible and relatively inexpensive multi-source collaborative variable data, and corrects the interpolation weight ratio of IDW interpolation at the position of the three-dimensional grid to be interpolated through the Mahalanobis distance of the multi-source collaborative variables in the attribute space, thereby realizing the improvement of the spatial interpolation accuracy of pollutant concentration and the accurate description of the spatial distribution details. This has broad application prospects for the pollution risk assessment and mapping of sites with sparse boreholes.

[0095] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A three-dimensional spatial interpolation method for soil pollutant concentrations in a site that integrates multi-source collaborative variables, characterized in that: Through steps A to G, a three-dimensional interpolation model of soil pollutant concentrations in the target area is obtained, and through step i, the three-dimensional interpolation model of soil pollutant concentrations is applied to predict the three-dimensional distribution of soil pollutant concentrations in the underground space of the target area; Step A. Obtain the measured values of soil pollutant concentrations of soil sample points at each preset depth under each preset drilling position in the target area, and a multi-source collaborative variable data set corresponding to the target area that includes each preset data type, and then enter step B; Step B. Based on the three-dimensional rasterized underground space preset in the target area, obtain the multi-source collaborative variable data sets corresponding to each grid in the underground space of the target area, and use the principal component analysis method to obtain the scores of the principal components of each collaborative variable in the multi-source collaborative variable data set. Furthermore, according to the positions of the soil sample points, obtain the scores of the principal components of each collaborative variable corresponding to each soil sample point, and then enter step C; Step C. Based on each soil sample point, perform stepwise regression analysis with the scores of the principal components of each collaborative variable corresponding to the soil sample point as the independent variable and the measured value of the soil pollutant concentration as the dependent variable, screen the principal component data of each collaborative variable, and obtain each principal component that is significantly correlated with the soil pollutant concentration, constituting each collaborative variable, and then enter step D; Step D. Based on each collaborative variable, obtain the collaborative variable vectors composed of the collaborative variable data corresponding to each grid, and obtain the collaborative variable vectors composed of the collaborative variable data corresponding to each soil sample point, and then enter step E; Step E. Obtain the Mahalanobis distances between the collaborative variable vectors corresponding to each grid and the collaborative variable vectors corresponding to each soil sample point, and obtain the three-dimensional Euclidean distances between each grid and each soil sample point, and then enter step F; Step F. According to each Mahalanobis distance, each three-dimensional Euclidean distance, and the weight ratio parameter α and the distance power parameter p, construct a three-dimensional interpolation model of soil pollutant concentrations, and then enter step G; Step G. Use the simulated annealing algorithm to optimize and obtain the value of the weight ratio parameter α and the value of the distance power parameter p in the three-dimensional interpolation model of soil pollutant concentrations, that is, obtain the three-dimensional interpolation model of soil pollutant concentrations corresponding to the target area; Step i. For each grid in the underground space of the target area respectively, apply the three-dimensional interpolation model of soil pollutant concentrations to obtain the predicted value of the soil pollutant concentration of the grid, that is, realize the three-dimensional prediction of the soil pollutant concentration in the underground space of the target area.

2. The three-dimensional spatial interpolation method for soil pollutant concentrations in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: It also includes step H as follows. After step G is executed, enter step H; Step H. Apply the cross-validation method to calculate the root mean square error between the predicted value of the soil pollutant concentration of the soil sample point obtained based on the three-dimensional interpolation model of soil pollutant concentrations and its corresponding measured value of the soil pollutant concentration, that is, obtain the interpolation accuracy of the three-dimensional interpolation model of soil pollutant concentrations.

3. The three-dimensional spatial interpolation method for the concentration of soil pollutants in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: the preset data types included in the multi-source collaborative variable dataset are the type distribution of site functional areas, the soil resistivity distribution inverted by geophysical exploration, and the soil conductivity distribution inverted by geophysical exploration.

4. The three-dimensional spatial interpolation method for the concentration of soil pollutants in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: step E includes the following steps E1 to E2: Step E1. First, for each grid in the underground space of the target area, according to the following formula: Obtain the Mahalanobis distance (MD ij ) I×J between the co-variable vectors corresponding to each grid and the co-variable vectors corresponding to each soil sample point, where i = 1, 2, ..., I, I represents the number of grids in the underground space of the target area, j = 1, 2, ..., J, J represents the number of soil sample points in the target area, cov i represents the co-variable vector corresponding to the i-th grid in the underground space of the target area, cov j represents the co-variable vector corresponding to the j-th soil sample point in the target area, ∑ represents the covariance matrix, (·) T represents the transpose, and MD ij represents the Mahalanobis distance between the co-variable vector corresponding to the i-th grid in the underground space of the target area and the co-variable vector corresponding to the j-th soil sample point in the target area; At the same time, for each grid in the underground space of the target area, according to the following formula: Obtain the three-dimensional Euclidean distance (ED ij ) I×J , where (x 1，i , x 2，i , x 3，i ) represents the three-dimensional coordinates of the i-th grid in the underground space of the target area, and (y 1，j , y 2，j , y 3，j ) represents the three-dimensional coordinates of the j-th soil sample point in the target area; then proceed to step E2; Step E2. Normalize each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J to the same scale, and update each Mahalanobis distance (MD ij ) I×J and each Euclidean distance (ED ij ) I×J , then proceed to Step F.

5. The three-dimensional spatial interpolation method for the concentration of soil pollutants in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: In step F, according to each Mahalanobis distance (MD ij ) I×J , each Euclidean distance (ED ij ) I×J , and the weight ratio parameter α and the distance power parameter p, the following three-dimensional interpolation model of soil pollutant concentration is constructed: Then enter step G, where P i represents the predicted value of the soil pollutant concentration of the i-th grid in the underground space of the target area, and V j represents the measured value of the soil pollutant concentration of the j-th soil sample point in the target area.

6. The three-dimensional spatial interpolation method for the concentration of soil pollutants in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: in step G, based on the prior value range [1, 3] of the distance power parameter p and the prior value range [0, 1] of the weight ratio parameter α, the simulated annealing algorithm is used to optimize and obtain the value of the weight ratio parameter α and the value of the distance power parameter p in the three-dimensional interpolation model of soil pollutant concentration.

7. The three-dimensional spatial interpolation method for the concentration of soil pollutants in a site that integrates multi-source collaborative variables according to claim 1, characterized in that: in step i, during the process of applying the three-dimensional interpolation model of soil pollutant concentration to realize the prediction of the soil pollutant concentration in the underground space of the target area, if the Euclidean distance between the grid and the soil sample point closest to it and the Mahalanobis distance between the collaborative variables are both less than or respectively equal to the preset corresponding thresholds, then the measured value of the soil pollutant concentration of this soil sample point is defined as the predicted value of the soil pollutant concentration of this grid.

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